Discrete-Time Model of an Exploited Population with Age and Sex Structures: Instability and the Hydra Effect

Abstract

This study proposes a discrete-time mathematical model to investigate the impact of selective harvesting on the dynamics of a population with age and sex structures. The model assumes that the birth rate depends on the sex ratio of the population and the number of breeding pairs. The growth rate is regulated by limiting juvenile survival, where an increase in population size decreases the survival of immature individuals. We consider the following selective proportional exploitation: harvesting of juveniles and harvesting of mature males. Depending on the values of population parameters, selective harvesting can lead to the stabilization of population dynamics by dampening oscillations or the emergence and amplification of fluctuations in population size. The model reveals multistability domains in which different dynamic modes coexist, and variations in initial conditions can lead to changes in dynamic modes. Depending on the values of the population parameters, the proposed models with harvest reveal the hydra effect, indicating an increase in the equilibrium abundance of the exploited group after reproduction but before harvesting, with an increase in the harvesting rate. Selective harvesting, resulting in the hydra effect, increases the remaining population size due to reproduction and the number of harvested individuals.

Keywords

• discrete-time model
• age and sex structures
• density-dependent regulation
• selective harvesting
• stability
• dynamic modes